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# Circumference of a Circle

The perimeter of a circle is called the circumference of a circle.

But it is not easy to find the circumference of a circle because the boundary is not made of straight lines or edges. This problem of calculating the circumference of a circle has puzzled mathematicians for centuries. It was known in ancient Egypt that the distance around the boundary of a circle was directly linked to the length of its diameter.

This relationship, expressed as  results in a number (called pi) with a value of =  3.141 592 653 589 793 238 462 643 383 279 ….

This number continues forever without repetition and does not have a pattern that repeats. It is important to note that is an irrational number as it does not have an exact fraction or decimal value.

Over the centuries, many people have tried to express as a fraction. In ancient Egypt (around 1700 BC), ~ 3.1605 was used to estimate . In ancient Greece, the great mathematician Archimedes (around 225 BC) stated that the value of lay between 3 and 3 . The famous Chinese mathematician Tsu Ch’ung-chih (circa 470 AD) gave the value of as , which is accurate to 6 decimal places. In the 13th century, Fibonacci estimate the value as ~ 3.14 8…

However, today the commonly used approximations for is as a fraction, and 3.14 as a decimal.

If you are using a scientific calculator, the value of should be obtained by pressing the key, unless otherwise indicated. is used in most calculations involving circles and cylinders.

## Formula for circumference of a circle

As discussed above, Rearranging this, we get the formula for circumference C = In other words, the circumference of a circle is obtained by multiplying and the diameter (d) of the circle.

This formula can be expressed in terms of the radius, r as:

C  = = (since d = 2r)

=   C  = C  = Now let us look at a few examples:

1. What is the circumference of this circle? C  = = =  44 cm

2. Calculate the circumference of the circle, correct to 1 decimal place. C  = = = =  56.5 cm

Note: In this example, the circumference could also be expressed as We’ll look at calculating the area of a circle.